Amorphous oxide semiconductors (AOS) are important candidates for next generation display transistors, but instability under illumination with month-long transients is a significant drawback and may limit broader use. Several models have been developed to fit transient photoconductivity observed in AOS and relate it to a spectrum of weighted time constants, equivalent to either a density of states distribution of deep traps within the activated energy model, or to a time-dependent relaxation time constant in other models. In this work, we classify fits of the time constant spectrum to the transient data as either “descriptive” if they make no presumption about the spectral shape, or “predictive” if they assume a spectral shape a priori characterized by a few simple parameters. By fitting both descriptive and predictive models to simulated transients, it is observed that the best fit converges for the descriptive model if the measurement duration exceeds the mode (“peak”) value of the time constant distribution. The predictive models can converge orders of magnitude faster, but rely on a proper identification of the correct lineshape a priori. Therefore, it is recommended that first an unbiased descriptive model of sufficient measurement duration be performed. Then the known lineshape can be applied as a predictive model for future measurements, reducing subsequent measurement durations by orders of magnitude.